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Introduction to particle physics

Physics 129, Fall 2010; Prof. D. Budker . Introduction to particle physics. Some introductory thoughts. Reductionists’ science Identical particles are truly so (bosons, fermions) We will be using (relativistic) QM where initial conditions do not uniquely define outcome:. Units.

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Introduction to particle physics

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  1. Physics 129, Fall 2010; Prof. D. Budker Introduction to particle physics

  2. Some introductory thoughts • Reductionists’ science • Identical particles are truly so (bosons, fermions) • We will be using (relativistic) QM where initial conditions do not uniquely define outcome: Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  3. Units • We use Gaussian units, thank you, Prof. Griffiths! Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  4. Useful resource: • Particle Data Group: http://pdg.lbl.gov/ • The Particle Data Group is an international collaboration charged with summarizing Particle Physics, as well as related areas of Cosmology and Astrophysics. In 2008, the PDG consisted of 170 authors from 108 institutions in 20 countries. • Order your free Particle Data Booklet ! Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  5. The Standard Model Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  6. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  7. The Standard Model Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  8. The Standard Model Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  9. The Standard Model Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  10. The Standard Model Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  11. Composite particles: it’s like Greek to me Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  12. In the beginning… • First 4 chapters in Griffiths --- self review • We will cover highlights in class • Homework is essential! • Physics Department colloquia and webcasts • Watch Frank Wilczek’s Oppenheimer lecture • Take advantage of being at Berkeley! Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  13. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  14. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  15. The Universe today: little do we know! Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  16. NuclearPhysics Atomic Physics ParticlePhysics CM Physics Cosmology Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  17. Particle colliders: the tools of discovery PDG collider table CERN LHC video Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  18. Particle detectors: the tools of discovery Atlas detector: assembly First Ze+e- event at Atlas Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  19. Feynman diagrams Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  20. Feynman diagrams Professor Oleg Sushkov’s notes, pp. 36-42: http://www.phys.unsw.edu.au/PHYS3050/pdf/Particles_classification.pdf Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  21. Feynman diagrams Oleg Sushkov Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  22. Feynman diagrams Oleg Sushkov Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  23. Feynman diagrams Oleg Sushkov Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  24. Feynman diagrams Oleg Sushkov Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  25. Running coupling constants Renormalization……unification? * No hope of colliders at 1014GeV !  need to learn to be smart! Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  26. The atmospheric muon “paradox” Mean lifetime: = 2.19703(4)×10−6 s c   6×104 cm = 600 m How do muons reach sea level?  Relativistic time dilation Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  27. Lorentz transformations Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  28. Lorentz transformations: adding velocities Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  29. By the way… • If we fire photons heads on, what is their relative speed? • Moving shadows, scissors,… • Garbage (IMHO):superluminal tunneling • Confusing terminology (IMHO): “fast light” Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  30. Lorentz transformations: Griffiths’ 3 things to remember • Moving clocks are slower (by a factor of  > 1) • Moving sticks are shorter (by a factor of  > 1) Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  31. Lorentz transformations: seen as hyperbolic rotations Rapidities: x moving α stationary t Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  32. Symmetries, groups, conservation laws Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  33. Symmetries, groups, conservation laws • Symmetry: operation that leaves system “unchanged” • Full set of symmetries for a given system  GROUP • Elements commute  Abelian group • Translations – abelian; rotations – nonabelian • Physical groups – can be represented by groups of matrices • U(n) – n  n unitary matrices: • SU(n) – determinant equal 1 • Real unitary matrices: O(n) • SO(n) – all rotations in space of n dimensions • SO(3) – the usual rotations (angular-momentum conservation) Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  34. Angular Momentum • First, a reminder from Atomic Physics Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html

  35. Angular momentum of the electron in the hydrogen atom • Orbital-angular-momentum quantum numberl = 0,1,2,… • This can be obtained, e.g., from the Schrödinger Eqn., or straight from QM commutation relations • The Bohr model: classical orbits quantized by requiring angular momentum to be integer multiple of  • There is kinetic energy associated with orbital motion  an upper bound on lfor a given value of En • Turns out: l = 0,1,2, …, n-1

  36. Angular momentum of the electron in the hydrogen atom (cont’d) • In classical physics, to fully specify orbital angular momentum, one needs two more parameters (e.g., two angles) in addition to the magnitude • In QM, if we know projection on one axis (quantization axis), projections on other two axes are uncertain • Choosing z as quantization axis: • Note: this is reasonable as we expect projection magnitude not to exceed

  37. Angular momentum of the electron in the hydrogen atom (cont’d) • m – magnetic quantum number because B-field can be used to define quantization axis • Can also define the axis with E (static or oscillating), other fields (e.g., gravitational), or nothing • Let’s count states: • m = -l,…,l i. e. 2l+1 states • l = 0,…,n-1 

  38. Angular momentum of the electron in the hydrogen atom (cont’d) • Degeneracy w.r.t. m expected from isotropy of space • Degeneracy w.r.t. l, in contrast,is a special feature of 1/r (Coulomb) potential

  39. Angular momentum of the electron in the hydrogen atom (cont’d) • How can one understand restrictions that QM puts on measurements of angular-momentum components ? • The basic QM uncertainty relation(*) leads to (and permutations) • We can also write a generalizeduncertainty relation between lzand φ(azimuthal angle of the e): • This is a bit more complex than (*) because φis cyclic • With definite lz ,

  40. Wavefunctions of the H atom • A specific wavefunction is labeled with n l m : • In polar coordinates : i.e. separation of radial and angular parts • Further separation: Spherical functions (Harmonics)

  41. Wavefunctions of the H atom (cont’d) Legendre Polynomials

  42. Electron spin and fine structure • Experiment: electron has intrinsic angular momentum --spin (quantum number s) • It is tempting to think of the spin classically as a spinning object. This might be useful, but to a point Experiment: electron is pointlike down to ~ 10-18 cm

  43. Electron spin and fine structure (cont’d) • Another issue for classical picture: it takes a 4πrotation to bring a half-integer spin to its original state. Amazingly, this does happen in classical world: from Feynman's 1986 Dirac Memorial Lecture (Elementary Particles and the Laws of Physics, CUP 1987)

  44. Electron spin and fine structure (cont’d) • Another amusing classical picture: spin angular momentum comes from the electromagnetic field of the electron: • This leads to electron size Experiment: electron is pointlike down to ~ 10-18 cm

  45. Electron spin and fine structure (cont’d) • s=1/2  • “Spin up” and “down” should be used with understanding that the length (modulus) of the spin vector is >/2 ! • The square of the projection is always 1/4

  46. Electron spin and fine structure (cont’d) • Both orbital angular momentum and spin have associated magnetic momentsμl and μs • Classical estimate of μl : current loop • For orbit of radius r, speed p/m, revolution rate is Gyromagnetic ratio

  47. Electron spin and fine structure (cont’d) • In analogy, there is also spin magnetic moment : Bohr magneton

  48. Electron spin and fine structure (cont’d) • The factor 2 is important ! • Dirac equation for spin-1/2 predicts exactly 2 • QED predicts deviations from 2 due to vacuum fluctuations of the E/M field • One of the most precisely measured physical constants: 2=2 1:001 159 652 180 73 28 [0.28 ppt] Prof. G. Gabrielse, Harvard

  49. Electron spin and fine structure (cont’d)

  50. Electron spin and fine structure (cont’d) • When both l and s are present, these are not conserved separately • This is like planetary spin and orbital motion • On a short time scale, conservation of individual angular momenta can be a good approximation • l and sare coupled via spin-orbit interaction: interaction of the motional magnetic field in the electron’s frame with μs • Energy shift depends on relative orientation of l and s, i.e., on

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